102 PART 3 Getting Down and Dirty with Data

Looking at Levels of Measurement

Around the middle of the 20th century, the idea of levels of measurement caught

the attention of biological and social-science researchers and, in particular, psy-

chologists. One classification scheme, which has become widely used (at least in

statistics textbooks), recognizes four levels at which variables can be measured:

nominal, ordinal, interval, and ratio:»

» ^{Nominal variables are expressed as mutually exclusive categories, like}

country of origin (United States, China, India, and so on), type of care provider

(nurse, physician, social worker, and so on), and type of bacteria (such as

coccus, bacillus, rickettsia, mycoplasma, or spirillum). Nominal indicates that

the sequence in which you list the different categories is purely arbitrary. For

example, listing type of care provider as nurse, physician, and social worker

is no more or less natural than listing them as social worker, nurse, and

physician.»

» ^{Ordinal data have categorical values (or levels) that fall naturally into a logical}

sequence, like the severity of cancer (Stages I, II, III, and IV), or an agreement

scale (often called a Likert scale) with levels of strongly disagree, somewhat

disagree, neither agree nor disagree, somewhat agree, or strongly agree. Note

that the levels are not necessarily equally spaced with respect to the concep-

tual difference between levels.»

» ^{Interval data represents numerical measurements where, unlike with ordinal}

classifications, the difference (or interval) between two numbers is a meaning-

ful measure in terms of being equally spaced, but the zero point is completely

arbitrary and does not denote the complete absence of what you’re measur-

ing. For example, a change from 20 to 25 degrees Celsius represents the

same amount of temperature increase as a change from 120 to 125 degrees

Celsius. But 0 degrees Celsius is purely arbitrary — it does not represent the

total absence of temperature; it’s simply the temperature at which water

freezes (or, if you prefer, ice melts).»

» ^{Ratio data, unlike interval data, does have a true zero point. The numerical}

value of a ratio variable is directly proportional to how much there is of what

you’re measuring, and a value of zero means there’s nothing at all. Income

and systolic blood pressure are good examples of ratio data; an individual

without a job may have zero income, which is not as bad as having a systolic

blood pressure of 0 mmHg, because then that individual would no longer be

alive!

Statisticians may pontificate about levels of measurement excessively, pointing out

cases that don’t fall neatly into one of the four levels and bringing up various

counterexamples. Nevertheless, you need to be aware of the concepts and termi-

nology in the preceding list because you’ll see them in statistics textbooks and